Parton distribution functions of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:math> on the lattice
Yahui Chai, Yuan Li, Shicheng Xia, Constantia Alexandrou, Krzysztof Cichy, Martha Constantinou, Xu Feng, Kyriakos Hadjiyiannakou, Karl Jansen, Giannis Koutsou, Chuan Liu, Aurora Scapellato, Fernanda Steffens
Abstract
We perform a first calculation for the unpolarized parton distribution function of the ${\mathrm{\ensuremath{\Delta}}}^{+}$ baryon using lattice QCD simulations within the framework of large momentum effective theory. Two ensembles of ${N}_{f}=2+1+1$ twisted mass fermions are utilized with a pion mass of 270 and 360 MeV, respectively. The baryon, which is treated as a stable single-particle state, is boosted with momentum ${P}_{3}$ with values ${0.42,0.83,1.25}\text{ }\text{ }\mathrm{GeV}$, and we utilize momentum smearing to improve the signal. The unpolarized parton distribution function of ${\mathrm{\ensuremath{\Delta}}}^{+}$ is obtained using a nonperturbative renormalization and a one-loop formula for the matching, with encouraging precision. In particular, we compute the $\overline{d}(x)\ensuremath{-}\overline{u}(x)$ asymmetry and compare it with the same quantity in the nucleon, in a first attempt towards resolving the physical mechanism responsible for generating such asymmetry.